Method and Arrangement Relating to Telecommunications

ABSTRACT

The present invention relates to a method and arrangement for providing a reliability information on information bits (bk) transmitted in a communications network, said bits constituting a transmitted vector (s) comprising elements selected by a transmitter from finite alphabet (S), wherein said transmitted vector is detected from an observed vector received symbols (y) providing a log-likelihood (L). Thus, the approximation is done by defining a number of bit terms having constant size and selecting a subset of bits and marginalizing over a selected part of said subset of bits.

TECHNICAL FIELD

The present invention relates to communications network and especiallycommunications network in which a number of transmit and receiveantennas are used.

BACKGROUND OF THE INVENTION

The existing wireless mobile communication systems provide several typesof services and mostly depend on channel coding to overcome anyinferiority of channels. However, due to the increasing demands, forexample for high-quality multimedia services, in which users cancommunicate with anyone regardless of time and place, the existingservices have evolved data-oriented services. Accordingly, there is ahigh demand for next generation wireless transmission technology fortransmitting the larger amount of data at a lower error rate. Inparticular, it is very important to transmit data at a high rate in alink is in which the amount of required data is large.

For the next generation wireless communications, various antenna systemshave been proposed. For example, a Multiple Input, Multiple output(MIMO) system, i.e., a typical antenna system, increases spectrumefficiency through all of transmission antennas without excessive use ofa frequency bandwidth. Generally, MIMO is classified into Space-TimeCoding (STC), Diversity, Beam Forming (BF), and Spatial Multiplexing(SM) according to the transmission structure and scheme of atransmitter, all of which provide high data rate and reliability.

A MIMO system adopts multiple antennas or array antenna totransmit/receive data in the transmitter and receiver. Multiple antennasare provided in different spatial positions, with different fadingfeatures, thus the received signals of adjacent antennas can beapproximated as uncorrelated entirely as long as the spacing betweenadjacent antennas for transmitting/receiving signals in the MIMO systemis large enough. The MIMO system takes full advantage of the spatialcharacteristics of multipath for implementing space diversitytransmission and reception.

FIG. 1 illustrates an exemplary and simplified MIMO system 100constructed by M Tx antennas 103 and N Rx antennas 104. As mentionedearlier, the antenna spacing between the Tx antennas and Rx antennas inthe MIMO system in FIG. 1 is generally big enough, to guarantee thespatial un-correlation of signals. As FIG. 1 shows, in the transmitter,MIMO architecture unit 101 first transforms a channel of data streaminto M channels of parallel sub data streams; then, multiple accesstransform unit 102 performs multiplex processing; finally, thecorresponding M Tx antennas 103 transmit the signal simultaneously intothe wireless channels. The MIMO architecture unit 101 can adopt any oneof the MIMO processing methods, such as STTC (Space Time Trellis Code),space-time block code, space-time Turbo code, BLAST code and etc. Whilemultiple access transform unit 102 can implements TDD, FDD or CDMA.Efficient demodulation of MIMO is non-trivial and currently a hotresearch topic.

In many communications receivers there is a need to separate multiplesymbols that have undergone mixing due to a channel that introducescross-talk. In particular, this is a key problem for MIMO receiverswhere this mixing is induced by the propagation channel. A commonmathematical model for such a cross-talk channel is:

y=Hs+e  (1)

wherein

-   -   s is a transmitted vector (of length n_(t)). The vector s has        elements that are chosen by the transmitter from a finite        alphabet S (Quadrature Amplitude Modulation (QAM) for example),    -   H is a channel matrix of dimension n_(r)×n_(t), where n_(r) is        the number of receive antennas and n_(t) the number of transmit        antennas, and    -   e is a vector of additive Gaussian noise.

The model (1) is general enough to also describe MIMO Systems that use(not-necessarily orthogonal) Space-Time Block Coding (STBC), byappropriately using a structured matrix H.

The receiver must detect s from an observed y. In systems that useChannel coding of any sort (convolutional, turbo, etc.) it is also ofinterest to compute soft decisions (reliability information) on theinformation bits b_(k,i) that constitute s. One can show [1] that if allsymbols are equally likely a priori this amounts to Computing

$\begin{matrix}{{L\left( b_{k,i} \middle| y \right)} = {\log\left( \frac{\sum_{{s\text{:}{b_{k,i}{(s)}}} = 1}{\exp \left( {{- \frac{1}{N_{0}}}{{y - {Hs}}}^{2}} \right)}}{\sum_{{s:{b_{k,i}{(s)}}} = 0}{\exp \left( {{- \frac{1}{N_{0}}}{{y - {Hs}}}^{2}} \right)}} \right)}} & (2)\end{matrix}$

where N₀ is the power spectral density of the noise. Here b_(k,i) (s) isthe ith information bit of the kth element of the transmitted vector s.The notation s: b_(k,i) (s)=β means the set of all vectors s for whichb_(k,i) equals β.

Evaluation of (2) amounts to marginalizing a probability densityfunction and this can be done in a brute-force manner. The problemhowever is that this has too high complexity to be useful in practice.More precisely evaluating (2) requires O(2^(mn) ^(t) ) operations wherem is the number of bits per symbol in s. Even with hardware in theforeseeable future this is not possible to implement even for moderatelylarge n_(t).

Previous approaches to this problem include various approximations to(2). In the following some known approaches are presented along with adiscussion of their main drawbacks:

-   -   Log-max approximation. This approximates the two sums in (2)        with their largest term:

$\begin{matrix}{{L\left( b_{k,i} \middle| y \right)} \approx {\log\left( \frac{\max_{{s:{b_{k,i}{(s)}}} = 1}{\exp \left( {{- \frac{1}{N_{0}}}{{y - {Hs}}}^{2}} \right)}}{\max_{{s:{b_{k,i}{(s)}}} = 0}{\exp \left( {{- \frac{1}{N_{0}}}{{y - {Hs}}}^{2}} \right)}} \right)}} & (3)\end{matrix}$

The problems with this approach include:

-   -   There is a Performance loss associated with discarding all but        one term in the sum.    -   Finding the maximum term in the sum requires solving an integer        constrained least-squares problem. The best known technique for        this is the sphere decoding algorithm [2] and its relatives,        which has an average complexity that grows exponentially with        n_(t) [3]. Additionally, its complexity is random in the sense        that the number of operations needed to compute (3) will be        different for each received vector y. This presents a serious        problem for implementation, as it requires either hardware        designed for worst-case complexity, or data buffers of various        kinds. The sequential structure of the sphere decoding algorithm        also seriously limits the amount of parallelization which can be        achieved when the algorithm is implemented in an ASIC.    -   List-sphere-decoding [4]. The idea is to approximate the sums        in (2) with a sum over a subset of the terms, namely the terms        encountered when running the so-called sphere decoding        algorithm.

The problems with this approach are

-   -   There is a Performance loss associated with discarding all but a        subset of terms in the sum.    -   1. The sphere decoding algorithm and its relatives have an        expected complexity exponential in n_(t) [3]. Additionally its        complexity is random and the list-sphere decoder inherits the        implementational issues of the original sphere decoder.    -   2. There is an issue relating to how various parameters of the        algorithm should be selected in order for the subsets (over        which the sums in (2) are computed) to always contain at least        one member.    -   Heuristic approximations based on linear preprocessing of the        data. The problems with this approach is very poor to        unacceptable Performance on slow fading Channels

SUMMARY OF THE INVENTION

The present invention presents a computationally simple solution to theproblem of providing high-quality soft decisions, especially in MIMOsystems. The method according to the invention has fixed (i.e.non-random) complexity, i.e. the number of operations required perreceived bit does not depend on the channel or noise realization. Thismakes the technique, amongst others, to:

-   -   3. avoid random decoding delays;    -   4. suitable for implementation, especially in parallelized        hardware; and    -   5. stand out from competing Solutions based on various flavors        of sphere decoding, which has random complexity.

These objectives are achieved using a method for providing a reliabilityinformation on information bits transmitted in a communications network.The bits constituting a transmitted vector comprise elements selected bya transmitter from a finite alphabet. The transmitted vector is detectedfrom an observed vector of received symbols providing a log-likelihood.The method comprises: approximating the log-likelihood by defining anumber of bit terms having constant size and selecting a subset of bitsand marginalizing over a selected part of the subset of bits.

In the most preferred embodiment the approximation comprises:

$\begin{matrix}{{L\left( b_{k} \middle| y \right)} \approx {\log \left( \frac{\begin{matrix}{\sum\limits_{b_{I_{1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} {\sum\limits_{b_{I_{k - 1}} = 0}^{1}{\sum\limits_{b_{I_{k + 1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} \sum\limits_{b_{I_{r}} = 0}^{1}}}}}} \\\left( {\max\limits_{b_{I_{r + 1}},\; \ldots \mspace{11mu},b_{I_{n_{t}m}}}{\mu \begin{pmatrix}{b_{I_{1}},\ldots \mspace{14mu},b_{I_{k - 1}},1,} \\{b_{I_{k + 1}},\ldots \mspace{14mu},b_{I_{n_{t}m}}}\end{pmatrix}}} \right)\end{matrix}}{\begin{matrix}{\sum\limits_{b_{I_{1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} {\sum\limits_{b_{I_{k - 1}} = 0}^{1}{\sum\limits_{b_{I_{k + 1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} \sum\limits_{b_{I_{r}} = 0}^{1}}}}}} \\\left( {\max\limits_{b_{I_{r + 1}},\; \ldots \mspace{11mu},b_{I_{n_{t}m}}}{\mu \begin{pmatrix}{b_{I_{1}},\ldots \mspace{14mu},b_{I_{k - 1}},0,} \\{b_{I_{k + 1}},\ldots \mspace{14mu},b_{I_{n_{t}m}}}\end{pmatrix}}} \right)\end{matrix}} \right)}} \\{{{For}\mspace{14mu} k} \leq r} \\{{L\left( b_{k} \middle| y \right)} \approx {\log \left( \frac{\begin{matrix}{\sum\limits_{b_{I_{1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} \sum\limits_{b_{I_{r}} = 0}^{1}}} \\\begin{pmatrix}\max\limits_{b_{I_{r + 1}},\; \ldots \mspace{11mu},b_{I_{k - 1}},b_{I_{k + 1}},\; \ldots \mspace{11mu},{b_{I}}_{n_{t}m}} \\{\mu \left( {b_{I_{1}},\ldots \mspace{14mu},b_{I_{k - 1}},1,b_{I_{k + 1}},\ldots \mspace{11mu},b_{I_{n_{t}m}}} \right)}\end{pmatrix}\end{matrix}}{\begin{matrix}{\sum\limits_{b_{I_{1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} \sum\limits_{b_{I_{r}} = 0}^{1}}} \\\begin{pmatrix}\max\limits_{b_{I_{r + 1}},\; \ldots \mspace{11mu},b_{I_{k - 1}},b_{I_{k + 1}},\; \ldots \mspace{11mu},{b_{I}}_{n_{t}m}} \\{\mu \left( {b_{I_{1}},\ldots \mspace{14mu},{b_{I}\; b_{I_{k + 1}}},\ldots \mspace{11mu},b_{I_{n_{t}m}}} \right)}\end{pmatrix}\end{matrix}} \right)}} \\{{{{{For}\mspace{14mu} k} > r},\mspace{14mu} {where}}{{\mu \left( {b_{0},\ldots \mspace{14mu},b_{n_{t}m}} \right)}\overset{\Delta}{=}{\exp \left( {{- \frac{1}{N_{0}}}{{y - {{Hs}\left( {b_{0},\ldots \mspace{14mu},b_{n_{t}m}} \right)}}}^{2}} \right)}}}\end{matrix}$

wherein

each bit in the vector (s) is enumerated as{b_(k)}_(k=1) ^(n) ^(t) ^(m),wherein n_(t) is the number of transmit antennas and m the number oftransmitted bits.

r is a fixed integer in an interval 0≦r≦n_(t)m−1

I is an index permutation on [1, . . . , n_(t)m] such that

enumerate the bits in increasing order of reliability,

k is 1≦k≦n_(t)m, and for a given k let k′ is a uniquely defined integersuch that I_(k′)=k, s(b₀, . . . , b_(ntm)) is the vector s whichcorresponds to the bits {b₁, . . . , b_(ntm)},

H is a channel matrix of dimension n_(r)×n_(t), where n_(r) number ofreceive and n_(t) transmit antennas, and

N₀ is power spectral density of noise.

Preferably, the maximum of μ(b₀, . . . , bn_(t)m) is obtained using alinear receiver followed by clipping. Preferably, for simplifying theapproximation, the marginalizing is over r-bits considered as inferiorbits. Yet, a further approximation may be applied by replacing themaxima with a simple, constant complexity estimate. Thus, the estimatemay be obtained by one of a zero forcing receiver, or nulling andcancelling.

Moreover, a bit ordering, I, is obtained by groping bits into symbolsand choosing a symbol ordering,

, according to a brute-force enumeration of all possible orderings:

 * = arg   max    cond  ( H _  ) , H _  = [ h   r  /  m + 1, …  , h  n t ] Eq .  1

where cond(.) refers to a condition number of a matrix. The bit orderingI may then be obtained from

by identifying to which symbol a particular bit is mapped. Thus,

is chosen by:

i. Letting

=[ ] and

=[1, . . . , 2 n_(t)].

ii. Computing γ=diag{( H ^(T) H)⁻¹}. Let i be the index of the largestelement of γ

iii. Setting

:=[

,

].

iv. Removing the ith column from H.

v. Removing the ith element of

.

vi. If H is empty, terminating otherwise repeating from step ii.

Moreover, Eq. 1 may be approximated where

is the index vector obtained by sorting diag{( H ^(T) H)⁻¹}.

In one embodiment, penalty factors that correspond to a prioriinformation on the bits that constitute s may be inserted.

The network may comprise a number of transmit and receive antennas,being one of Multiple-Input, Multiple-Output (MIMO),

The invention also relates to a communications network infrastructurearrangement comprising a computational device for providing areliability information on transmitted information bits. The bitsconstituting a transmitted vector (s) comprising elements selected by atransmitter from a finite alphabet (S). The transmitted vector may bedetected from an observed vector of received symbols (y) providing alog-likelihood (L). Thus, the device comprises a unit for detecting thetransmitted vector from an observed vector of received symbols, (y), aprocessing unit for applying approximation by defining a number of bitterms having constant size, a selector means for selecting a subset ofbits and calculation means for marginalizing over a selected part of thesubset of the bits. I one embodiment, the device further comprises alinear receiver followed by clipping or a decision feed-back typereceiver with optimal ordering. The linear receiver may use one of aZero Forcing (ZF) or Minimum Mean-Squared Error (MMSE).

The invention also relates to communications device comprising aprocessing unit handling communication data and communication controlinformation, a memory unit, an interface unit, a communication unit witha respective connecting interface and transmit receive antennas. Thedevice further comprises an arrangement for providing a reliabilityinformation on transmitted information bits, the bits constituting atransmitted vector comprising elements selected by a transmitter from afinite alphabet. The transmitted vector is detected from an observedvector of received symbols providing a log-likelihood. The communicationunit is operatively arranged to detect the transmitted vector from anobserved vector of received symbols. The processing unit is for applyingapproximation by defining a number of bit terms having constant size, aselector means for selecting a subset of bits and calculation means formarginalizing over a selected part of the subset of the bits.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following, the invention will be exemplified with reference tonumber of embodiments, as illustrated in the drawings, in which:

FIG. 1 is a schematic diagram of a MIMO system,

FIG. 2 illustrates a graph over a MIMO system with n_(t)=4 transmitantennas, n_(r)=4 receive antennas, QPSK modulation, slow Rayleighfading. Each codeword consists of 100 bits and spans one channelrealization,

FIG. 3 is a flow diagram illustrating the steps according to theinvention,

FIG. 4 is a block diagram illustrating an arrangement implementing theinvention, and

FIG. 5 is a block diagram illustrating a user unit implementing theinvention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present invention provides a new way to compute the followingapproximations of (2). In the following, to avoid working with doubleindices, all bits in s are enumerated as{b_(k)}_(k=1) ^(n) ^(t) ^(m),wherein n_(t) is the number of transmit antennas and m the number oftransmitted bits.

Let r be a fixed integer (user parameter) in the interval 0≦r≦n_(t)m−1.Let I be an index permutation on [1, . . . , n_(t)m] so that

enumerates the bits in increasing order of reliability, i.e. the mostuncertain bits first. Then for a given k, 1≦k≦n_(t)m, let k′ be theuniquely defined integer such that I_(k′)=k. We propose the followingapproximations:

$\begin{matrix}{{L\left( b_{k} \middle| y \right)} \approx {\log \left( \frac{\begin{matrix}{\sum\limits_{b_{I_{1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} {\sum\limits_{b_{I_{k - 1}} = 0}^{1}{\sum\limits_{b_{I_{k + 1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} \sum\limits_{b_{I_{r}} = 0}^{1}}}}}} \\\left( {\max\limits_{b_{I_{r + 1}},\; \ldots \mspace{11mu},b_{I_{n_{t}m}}}{\mu \begin{pmatrix}{b_{I_{1}},\ldots \mspace{14mu},b_{I_{k - 1}},1,} \\{b_{I_{k + 1}},\ldots \mspace{14mu},b_{I_{n_{t}m}}}\end{pmatrix}}} \right)\end{matrix}}{\begin{matrix}{\sum\limits_{b_{I_{1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} {\sum\limits_{b_{I_{k - 1}} = 0}^{1}{\sum\limits_{b_{I_{k + 1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} \sum\limits_{b_{I_{r}} = 0}^{1}}}}}} \\\left( {\max\limits_{b_{I_{r + 1}},\; \ldots \mspace{11mu},b_{I_{n_{t}m}}}{\mu \begin{pmatrix}{b_{I_{1}},\ldots \mspace{14mu},b_{I_{k - 1}},0,} \\{b_{I_{k + 1}},\ldots \mspace{14mu},b_{I_{n_{t}m}}}\end{pmatrix}}} \right)\end{matrix}} \right)}} & (4) \\{{{For}\mspace{14mu} k} \leq r} & \; \\{{L\left( b_{k} \middle| y \right)} \approx {\log \left( \frac{\begin{matrix}{\sum\limits_{b_{I_{1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} \sum\limits_{b_{I_{r}} = 0}^{1}}} \\\begin{pmatrix}\max\limits_{b_{I_{r + 1}},\; \ldots \mspace{11mu},b_{I_{k - 1}},b_{I_{k + 1}},\; \ldots \mspace{11mu},{b_{I}}_{n_{t}m}} \\{\mu \left( {b_{I_{1}},\ldots \mspace{14mu},b_{I_{k - 1}},1,b_{I_{k + 1}},\ldots \mspace{11mu},b_{I_{n_{t}m}}} \right)}\end{pmatrix}\end{matrix}}{\begin{matrix}{\sum\limits_{b_{I_{1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} \sum\limits_{b_{I_{r}} = 0}^{1}}} \\\begin{pmatrix}\max\limits_{b_{I_{r + 1}},\; \ldots \mspace{11mu},b_{I_{k - 1}},b_{I_{k + 1}},\; \ldots \mspace{11mu},{b_{I}}_{n_{t}m}} \\{\mu \left( {b_{I_{1}},\ldots \mspace{14mu},b_{I_{k - 1}},0,\; b_{I_{k + 1}},\ldots \mspace{11mu},b_{I_{n_{t}m}}} \right)}\end{pmatrix}\end{matrix}} \right)}} & (5) \\{{{{{For}\mspace{14mu} k} > r},\mspace{14mu} {where}}{{\mu \left( {b_{0},\ldots \mspace{14mu},b_{n_{t}m}} \right)}\overset{\Delta}{=}{\exp \left( {{- \frac{1}{N_{0}}}{{y - {{Hs}\left( {b_{0},\ldots \mspace{14mu},b_{n_{t}m}} \right)}}}^{2}} \right)}}} & \;\end{matrix}$

Here s(b₀, . . . , b_(ntm)) stands for the vector s which corresponds tothe bits {b₀, . . . , b_(ntm)}.

Simply, the invention implies defining a number of terms having constantsize and selecting a subset of bits and marginalize over a selected partof the said bits. Thus, the motivation of the approximations in (4) and(5) is that the typical errors encountered in the detection processoccur when the MIMO Channel degenerates in a few spatial dimensions. Bymarginalizing over the “worst” r-bits (as in done in (4) and (5)) thisproblem is effectively eliminated. Additionally, although it iscertainly possible for a large number of bits to simultaneously be ofpoor quality, such an event occurs less frequently and does notseriously affect the overall Performance. Similar behavior has beenobserved and quantified (in a theoretically rigorous fashion) in thecase of un-coded communication systems [5].

As is, approximations (4) and (5) are not efficiently computable due tothe inherent problem of solving the maxima in (4) and (5). Note thatthis is identical to the problem faced in log-max approximation in (3)and therefore implementing (4) and (5) directly would not circumventthis problem. Therefore, a further approximate (4) and (5) by replacingthe maxima with a simple, constant complexity, estimate such as forexample the estimate obtained by the zero forcing (hard decision)receiver, or nulling and cancelling.

A key aspect of the proposed approach is that replacing the maxima in(4) and (5) by the estimates obtained by a simple (i.e. Zero Forcing(ZF) or Minimum Mean-Squared Error (MMSE)) receiver will not degenerateperformance significantly if done correctly. The reason for this is thatthis (sub-optimal) approximation in only taken for the ‘“best” n_(t)m−rbits which are much easier to determine even for a sub-optimal detector.Assume now that r is an integer multiple of the number of bits persymbol which implies that full marginalization is done over fullsymbols. The ability of a suboptimal method to obtain the maxima in (4)and (5) is crucially dependent on the conditioning of the effectiveChannel matrix which is obtained when removing the “worst” r/m Symbols.Therefore, a good strategy is to find the worst r/m symbols (orequivalently r bits) by minimizing the resulting Channel matrixcondition number. To be specific, let

be an index permutation on [1, . . . , n_(t)], then the symbol orderingis found according to:

 * = arg   max    cond  ( H _  ) , H _  = [ h  r  /  m + 1 ,…  , h  n t ] . ( 6 )

where cond(.) refers to the condition number of a matrix. The bitordering

is then obtained from ζ by identifying to which symbol a particular bitis mapped. Further, since the maximum in (6) has to be found bysearching over

$\quad\begin{pmatrix}n_{t} \\{r\text{/}m}\end{pmatrix}$

candidate orderings, it will often make sense to use some form ofapproximation to (6).

Such an approximation may comprise the steps of:

is chosen 310 according to the algorithm (previously proposed and usedfor hard detection in [6]) given by:

320) Let

=[ ] and

=[1, . . . , 2 n_(t)].

330) Compute γ=diag{( H ^(T) H)}. Let i be the index of the largestelement of γ.

340) Set

:=[

,

].

350) Remove the ith column from H.

360) Remove the ith element of

.

370) If H is empty, terminate. Otherwise repeat from step 330).

(6) may also be approximated where

is the index vector obtained by sorting diag{( H ^(T) H)⁻¹}

Evidently, any other approximation of (6) may occur.

Expressions of type

$\log \left\{ {\sum\limits_{k}^{a_{k}}} \right\}$

can be evaluated by recursively applying identity log(e^(a)+e^(b))=max(a,b)+log(1+e^(−|a−b|)) and using a lookup-table the functionf(x)=log(1+e^(−|x|)) can be solved. The same is applicable to (4) and(5).

For the case of a separable constellation (such as rectangular QAM orQPSK) the model (1) may be equivalently formulated as

y= H s+ē  (7)

Where

${\overset{\_}{y} = \begin{bmatrix}{\; y} \\{\; y}\end{bmatrix}},{\overset{\_}{s} = \begin{bmatrix}{\; s} \\{\; s}\end{bmatrix}},{\overset{\_}{e} = \begin{bmatrix}{\; e} \\{\; e}\end{bmatrix}},{\overset{\_}{H} = \begin{bmatrix}{{\; H} - {\; H}} \\{\; H\mspace{14mu} \; H}\end{bmatrix}}$

In (7), all quantities are real-valued. Thus, with QPSK modulation, theelements of s are binary (they are ±1, up to a possible scaling factor).This means that each element of s corresponds to exactly one Informationbit. Using (7) allows for more flexibility in choosing r than for thecomplex valued equivalent model. Also, in the QPSK case it can beassumed that

=I since bits and (real valued) Symbols are interchangeable under (7).

The performance of the proposed soft demodulation technique isillustrated in FIG. 2 for a slow fading 4×4 MIMO System with QPSKmodulation and rate-⅓ convolutional coding. The Channel model isrewritten according to (7). There is a tradeoff between r and thePerformance obtained. The complexity is roughly 0(2^(r)n_(t)n_(r)). Theresults show that Performance is close to that of the brute-forcemaximum-a posteriori detector (2), even for small values of r.

The invention may be implemented as a hardware or software solution or acombination of these.

The invention may be implemented in a network node, which may comprise acomputer unit 400 for processing signals, as illustrated in FIG. 4. Thenetwork is assumed to have a number of transmit antennas transmittingn_(T) symbols, and in which x_(m), denotes symbols transmitted, whereinm=1 . . . n_(T). A symbol alphabet is assumed to contain L symbols. Thecomputer unit 400, as illustrated schematically in FIG. 4, may comprisea unit 410 for detecting the transmitted vector from an observed vectorof received symbols, y, a processing unit 420 for applying approximationby defining a number of bit terms having constant size stored in amemory 430 and a selector means 440 for selecting a subset of bits andcalculation means 450 for marginalizing over a selected part of thesubset of the bits.

More especially, the computing unit 400 according to one embodimentcomprises a linear receiver 460 output of which is coupled to a clipper470. The linear receiver may use a Zero Forcing (ZF) or MinimumMean-Squared Error (MMSE). In another embodiment a decision feed-backtype receiver 480 with optimal ordering can be used.

FIG. 5 illustrates in a schematic block diagram a user equipment (UE)500 implementing teachings of the present invention, wherein aprocessing unit 520 handles communication data and communication controlinformation. The UE 500 further comprises a volatile (e.g. RAM) 530and/or non volatile memory (e.g. a hard disk or flash disk) 540, aninterface unit 550. The UE 500 may further comprise a mobilecommunication unit 560 with a respective connecting interface. All unitsin the UE can communicate with each other directly or indirectly throughthe processing unit 570. Software for implementing the method accordingto the present invention may be executed within the UE 500. The UE 500may also comprise an interface 580 for communicating with anidentification unit, such as a SIM card, for uniquely identifying the UEin a network and for use in the identification of the ‘SIGN’ (i.e.traffic counting and digital signature of the UE). Other features oftenpresent in UE are not shown in FIG. 5 but should be understood by theperson skilled in the art, e.g. for a mobile phone: MIMO antennas 510,camera, replaceable memory, screen and buttons. The computer unitaccording FIG. 4 may be implemented as an additional part or part of theprocessing unit.

The invention is not limited to MIMO systems and may be implemented inany multiple transmit/receive systems such asSingle-Input-Multiple-Output (SIMO), Multiple-Input-Single-Output MISOetc.

The problem solved by the present invention is important for alldemodulation problems in the presence of cross-talk, with MIMO as anoutstanding example. For MIMO it is applicable both to systems that usespatial multiplexing (e.g. V-BLAST) [7] and space-time coding (forexample, linear dispersion codes [8]). Such systems are currentlyundergoing standardization.

The invention itself, however, is not limited to any particularstandard.

It should be noted that the word “comprising” does not exclude thepresence of other elements or steps than those listed and the words “a”or “an” preceding an element do not exclude the presence of a pluralityof such elements. The invention can at least in part be implemented ineither software or hardware. It should further be noted that anyreference signs do not limit the scope of the claims, and that several“means”, “devices”, and “units” may be represented by the same item ofhardware.

The above mentioned and described embodiments are only given as examplesand should not be limiting to the present invention. Other solutions,uses, objectives, and functions within the scope of the invention asclaimed in the below described patent claims should be apparent for theperson skilled in the art.

REFERENCES

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1. A method for providing a reliability information on information bits(b_(k)) transmitted in a communications network, said bits constitutinga transmitted vector (s) comprising elements selected by a transmitterfrom a finite alphabet (S), wherein said transmitted vector is detectedfrom an observed vector of received symbols (y) providing alog-likelihood (L), the method comprising: approximating saidlog-likelihood (L) by defining a number of bit terms having constantsize and selecting a subset of bits and marginalizing over a selectedpart of said subset of bits.
 2. The method of claim 1, wherein saidapproximation comprises: $\begin{matrix}{{L\left( b_{k} \middle| y \right)} \approx {\log \left( \frac{\begin{matrix}{\sum\limits_{b_{I_{1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} {\sum\limits_{b_{I_{k - 1}} = 0}^{1}{\sum\limits_{b_{I_{k + 1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} \sum\limits_{b_{I_{r}} = 0}^{1}}}}}} \\\left( {\max\limits_{b_{I_{r + 1}},\; \ldots \mspace{11mu},b_{I_{n_{t}m}}}{\mu \begin{pmatrix}{b_{I_{1}},\ldots \mspace{14mu},b_{I_{k - 1}},1,} \\{b_{I_{k + 1}},\ldots \mspace{14mu},b_{I_{n_{t}m}}}\end{pmatrix}}} \right)\end{matrix}}{\begin{matrix}{\sum\limits_{b_{I_{1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} {\sum\limits_{b_{I_{k - 1}} = 0}^{1}{\sum\limits_{b_{I_{k + 1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} \sum\limits_{b_{I_{r}} = 0}^{1}}}}}} \\\left( {\max\limits_{b_{I_{r + 1}},\; \ldots \mspace{11mu},b_{I_{n_{t}m}}}{\mu \begin{pmatrix}{b_{I_{1}},\ldots \mspace{14mu},b_{I_{k - 1}},0,} \\{b_{I_{k + 1}},\ldots \mspace{14mu},b_{I_{n_{t}m}}}\end{pmatrix}}} \right)\end{matrix}} \right)}} \\{{{For}\mspace{14mu} k} \leq r} \\{{L\left( b_{k} \middle| y \right)} \approx {\log \left( \frac{\begin{matrix}{\sum\limits_{b_{I_{1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} \sum\limits_{b_{I_{r}} = 0}^{1}}} \\\begin{pmatrix}\max\limits_{b_{I_{r + 1}},\; \ldots \mspace{11mu},b_{I_{k - 1}},b_{I_{k + 1}},\; \ldots \mspace{11mu},{b_{I}}_{n_{t}m}} \\{\mu \left( {b_{I_{1}},\ldots \mspace{14mu},b_{I_{k - 1}},1,b_{I_{k + 1}},\ldots \mspace{11mu},b_{I_{n_{t}m}}} \right)}\end{pmatrix}\end{matrix}}{\begin{matrix}{\sum\limits_{b_{I_{1}} = 0}^{1}\mspace{14mu} {\ldots \mspace{14mu} \sum\limits_{b_{I_{r}} = 0}^{1}}} \\\begin{pmatrix}\max\limits_{b_{I_{r + 1}},\; \ldots \mspace{11mu},b_{I_{k - 1}},b_{I_{k + 1}},\; \ldots \mspace{11mu},{b_{I}}_{n_{t}m}} \\{\mu \left( {b_{I_{1}},\ldots \mspace{14mu},{b_{I}\; b_{I_{k + 1}}},\ldots \mspace{11mu},b_{I_{n_{t}m}}} \right)}\end{pmatrix}\end{matrix}} \right)}} \\{{{{{For}\mspace{14mu} k} > r},\mspace{14mu} {where}}{{\mu \left( {b_{0},\ldots \mspace{14mu},b_{n_{t}m}} \right)}\overset{\Delta}{=}{\exp \left( {{- \frac{1}{N_{0}}}{{y - {{Hs}\left( {b_{0},\ldots \mspace{14mu},b_{n_{t}m}} \right)}}}^{2}} \right)}}}\end{matrix}$ wherein each bit in said vector (s) is enumerated as{b_(k)}_(k=1) ^(n) ^(t) ^(m), wherein n_(t) is the number of transmitantennas and m the number of transmitted bits, r is a fixed integer inan interval 0≦r≦n_(t)m−1 I is an index permutation on [1, . . . ,n_(t)m] such that

enumerate the bits in increasing order of reliability, k is 1≦k≦n_(t)m,and for a given k let k′ is a uniquely defined integer such thatI_(k)=k, s(b₀, . . . , b_(ntm)) is the vector s which corresponds to thebits {b₁, . . . , b_(ntm)}, H is a channel matrix of dimensionn_(r)×n_(t), where n_(r) number of receive and n_(t) transmit antennas,and N₀ is power spectral density of noise.
 3. The method of claim 2,wherein a maximum of μ(b_(o), . . . , bn_(t)m) is obtained using alinear receiver followed by clipping.
 4. The method of claim 2, whereinusing a decision feed-back type receiver with optimal ordering.
 5. Themethod of claim 3, wherein said linear receiver uses one of a ZeroForcing (ZF) or Minimum Mean-Squared Error (MMSE).
 6. The method ofclaim 2, wherein said marginalizing is over r-bits considered asinferior bits.
 7. The method of claim 2, comprising a furtherapproximation by replacing the maxima with a simple, constantcomplexity, estimate.
 8. The method of claim 6, wherein said estimate isobtained by one of a zero forcing receiver, or nulling and cancelling.9. The method of claim 2, wherein a bit ordering, I, is obtained bygroping bits into symbols and choosing a symbol ordering,

, according to a brute-force enumeration of all possible orderings:  * =arg   max    cond  ( H _    ) , H _    = [ h    r  / m + 1 , …  , h    n t ] . Eq .  1 where cond(.) refers to acondition number of a matrix.
 10. The method of claim 9, wherein the bitordering I is then obtained from

by identifying to which symbol a particular bit is mapped.
 11. Themethod of claim 9, wherein

is chosen by: i. Letting

=[ ] and

=[1, . . . , 2n_(t)]; ii. Computing γ=diag{( H ^(T) H)⁻¹} wherein i isthe index of the largest element of γ; iii. Setting

:=[

,

]; iv. Removing the ith column from H; v. Removing the ith element of

; and vi. If H is empty, terminating otherwise repeating from step ii.12. The method of claim 9, wherein Eq. 1 is approximated where

is the index vector obtained by sorting diag{( H ^(T) H)⁻¹}.
 13. Themethod of claim 2, comprising penalty factors that correspond to apriori information on the bits that constitute s.
 14. The methodaccording to claim 1, wherein said network comprises a number oftransmit and receive antennas, being one of Multiple-input,Multiple-Output (MIMO).
 15. A communications network infrastructurearrangement comprising a computational device for providing areliability information on transmitted information bits (b_(k)), saidbits constituting a transmitted vector (s) comprising elements selectedby a transmitter from a finite alphabet (S), wherein said transmittedvector is detected from an observed vector of received symbols (y)providing a log-likelihood (L), wherein said device comprises a unit fordetecting the transmitted vector from an observed vector of receivedsymbols, (y), a processing unit for applying approximation by defining anumber of bit terms having constant size, a selector means for selectinga subset of bits and calculation means for marginalizing over a selectedpart of the subset of the bits.
 16. The arrangement of claim 15, furthercomprising a linear receiver followed by clipping.
 17. The arrangementof claim 15, further comprising a decision feed-back type receiver withoptimal ordering.
 18. The arrangement of claim 16, wherein said linearreceiver uses one of a Zero Forcing (ZF) or Minimum Mean-Squared Error(MMSE).
 19. A communications device comprising a processing unithandling communication data and communication control information, amemory unity, an interface unit, a communication unit with a respectiveconnecting interface and transmit receive antennas, an arrangement forproviding a reliability information on transmitted information bits(b_(k)), which constitute a transmitted vector (s) detected from anobserved vector of received symbols (y) providing a log-likelihood (L),wherein said communication unit being operatively arranged to detect thetransmitted vector from an observed vector of received symbols, (y),said processing unit being operatively arranged for applyingapproximation by defining a number of bit terms having constant size, aselector means for selecting a subset of bits and calculation means formarginalizing over a selected part of the subset of the bits.
 20. Thecommunications device of claim 19, further comprising a linear receiverfollowed by clipping.
 21. The communications device of claim 19, furthercomprising a decision feed-back type receiver with optimal ordering. 22.The communications device of claim 20, wherein said linear receiver usesone of a Zero Forcing (ZF) or Minimum Mean-Squared Error (MMSE).